Question

Two wires A and B of same length and of the same material have the respective radii $r_{1}and{r}_2$. Their one end is fixed with a rigid support, and at the other ends equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and The angle of twist at the end of B will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Twisting couple $C=\frac{\pi \eta r^4\theta }{2l}$
If material and length of the wires A and B are equal and equal twisting couple are applied then
$\theta \propto \frac{1}{r^4}\therefore \frac{{\theta }_1}{{\theta }_2}=(\frac{r_2}{r_1}{)}^4$